Definition of a new static model of Parallel Kinematic Machines: Highlighting of overconstraint influence

This paper deals with static behaviour modelling of Parallel Kinematic Machines (PKMs). Due to their high dynamic abilities, PKMs are subjected to high inertial and cutting loads while machining. These loads generate structure deflection, and thus tool pose defects. The aim of this article is to present a predictable model of PKMs. This model could be useful to optimize part positioning in the workspace or adapt machining strategies in order to minimize the influence of structure deflections. The proposed model takes into account legs and joints compliances. Considering the geometry of most of parallel architectures, the legs are modelled as beams. The focus, here, is particularly on joint models. In the literature, when the compliance of joints is considered, it is always modelled with a constant stiffness. In this paper, a different approach is proposed, based on a technical analysis of the joints and non linear models are chosen. Models proposed are applied to an existing PKM: the Tricept. The parameters of this model (i.e. the stiffness of the joints) are then identified, thanks to experimental stiffness measurements done on a ABB 940 Tricept robot. Finally, a second architecture is studied. This machine is overconstrained even if it is very close to the Tricept architecture. The same modelling method is applied and the static behaviours of the two machines are compared. Thus, the effect of overconstraint on static behaviour is analysed.